Cable Velocity Factor

Velocity Factor in Cables

In theory, electrical signals move
at the speed of light. Cables only slow them down. The
ratio of actual speed to the speed of light is known
as the velocity factor, or Velocity of Propagation (VOP),
expressed as a percentage of the speed of light in free
space.

This slowing effect is almost entirely
caused by the dielectric material; in coaxial cables,
the insulation between the shield and the center conductor.
For a closed-cell foam dielectric, for example, the
VOP may approach 90%, meaning that a signal will travel
at 90% of the speed of light. For solid Teflon®,
the VOP is typically about 70%.

(These figures can differ according
to specific formulation of the material. They are also
subject to variation depending on the construction of
the cable.)

What effect does the VOP have? After
all, 70% of the speed of light is still pretty fast!
Fact is, in some avionic and other electronic applications,
speed and delay are critical factors and need to be
measured with precision.

The delay from one end of a cable to
the other is inversely proportional to the VOP: the
lower the VOP %, the longer the delay.

This can be important in relative signal
timing, for navigation systems, for example. Delay is
independent of frequency. In effect, it is the defining
factor of the electrical length of a wire or cable.

Published literature often lists
delay among the characteristics of cable. If so, it's
a simple matter to calculate the delay for a specific
length of cable based on the "ns/ft" value.
But it is also practical to calculate delay using the
VOP and the following formula:

...or, more practically,

where:d = Delay in nanosecondsL = Length of the cable in feetC = Velocity of light in free spaceVOP expressed in percent

As a guideline, Table
1 lists VOP, dielectric constant, and delay for
some of the common cable dielectric materials, along
with a few less common materials, included for your
amusement. Table 2 carries
this into
PIC coaxes and a few RG- types.

Delay is a critical factor in determining
the bearing of transponder signals received by a directional
TCAS antenna. But the figure of merit here is the absolute
phase angle of the cable at the specified frequency.

Wavelength & VOP

At
microwave frequencies (TCAS and transponders operate
near 1000 MHz), a single nanosecond (a billionth of
a second) is an entire wavelength. TCAS II tolerates
one such wavelength (360°) of mismatch among the
four upper or lower directional antenna cables, and
some TCAS I processors require even greater precision
than that. Note that such phase-matching requires not
only that the waves coincide in pattern with one another
from cable to cable but that they must do so within
the very same wave. (See Figure
1.) Thus both phase and delay measurements are
important.

At 100% VOP, the physical wavelength
at 1000 MHz (1.0 GHz) will be 11.80 inches. This can
be proportioned according to the cable's actual velocity
factor, as well as other frequencies. A practical formula
is:

It
needs to be understood, however, that even with the
relatively uniform VOP figures in a given cable type,
physically measuring them by the inch for phase-matching
is no assurance of an accurate match. This is because
actual VOP is not always exactly the published figure,
nor can it be considered perfectly uniform, even within
a single production run of cable. Variances are apt
to be more pronounced in cables having high VOP's. Only
test equipment which measures electrical length with
precision can verify meeting stringent standards such
as required for TCAS directional antennas.

PIC produces cables which meet and
exceed the requirements established for TCAS and other
RF systems. Precise testing is performed to assure that
crucial timing and phase- matching requirements are
met.

A related Issue: Dielectric Constant

This is a property of the material
itself — independent of dimensions — but
is an important factor in determining VOP and delay.

The word electric derives
from the Greek elektron, which translates to
amber. However, amber is an insulating material
and is known to produce an electric charge when rubbed.
And so even though we think of electric as inferring
the flow of electrons (current), we now know
that the term comes from some ancient insulator
(which has even been known to entomb prehistoric insects.
But that's another story — already made into a
hit movie or two.)

The prefix di- infers the
effect of preventing this flow. A dielectric (amber
would qualify) then, is a barrier — an insulator
— separating positive and negative electric charges
from one another, preventing direct current flow. This
action is typified by a capacitor.

In a cable, the dielectric is defined
as the non-conducting plastic or rubber (or even air)
which insulates a conductor from others.

No conductor material is perfect and
the same is true of insulation materials. There are
superconductors, special alloys which, in a very low
temperature environment, actually do exhibit zero resistance.
A perfect vacuum is also an absolute, but is as yet
unattainable. What about making cables using a perfect
vacuum as the insulation medium? It's even more impractical
than superconductors.

So, in the real world, while we might
quantify absolutes without practical access to them,
we can at least relate to them by a ratio. Thus defines
the dielectric constant (electrical symbol )
— the ratio of a material's dielectric (charge
storage) quality to that of a perfect vacuum. A perfect
vacuum is valued at 1.0. All other materials have a
greater value of .

For example, the dielectric constant
of solid PTFE (as used in RG142 and RG393) is nominally
2.1. This means that it will store about twice the charge
as a vacuum, or, put another way, roughly doubles the
capacitance. PIC's S33141 low-loss coaxial cable employs
a dielectric with an ? of about 1.8. It is lighter and
thinner but electrically equivalent to RG393, and the
dielectric constant is one reason why. Tables
1 & 2 above list these details.

The lower the dielectric constant,
the lower the loss, the lower the capacitance, the higher
the velocity of propagation — a cable which approaches
the ideal. But then we're talking superconductors with
a vacuum for insulation, or at least we are venturing
into currently impractical materials.

Some formulas for determining cable
parameters related to the dielectric constant are shown
below:

Calculating VSWR and loss, while the
dielectric constant is a factor, is not as straightforward.
For VSWR, it is also necessary to establish the reflection
impedance and, for loss, the stranding and braid factors
— all this being part of the cable design and
engineering process.

The dielectric constant is not the
only measure of quality of a cable; cellular polyethylene
has an
as low as 1.4, but it is rated at a lower temperature.
MIL-spec coaxes using polyethylene dielectrics (such
as RG58 and RG214) customarily also have PVC jackets
and are, therefore, unacceptable for aircraft applications
because of smoke and fire concerns.

But some newer techniques and chemistries
have developed — such things as foamed, wrapped
or expanded tape high-temperature dielectrics. All of
these reduce the dielectric constant; but, as increasing
amounts of air are incorporated, the material becomes
softer and there is a compromise with strength. A nice
solid extrusion of, say, PTFE is tough, but losses will
be greater than with expanded PTFE tape. Then again,
maybe it needs to be tough for practical or environmental
reasons.

The trade-offs begin. Electrical performance
vs. weight and strength — a never-ending concern
in the avionics industry. Cost figures in, too, but
often it is simply among the least of concerns.

For More Information

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